The present invention relates to a process for the production of carbon fibers wherein a prescribed amount of a particular chemical substance is fixed onto thermally stabilized fibers and/or carbonized fibers to give the fibers good filaments collectivity, and thereafter the fibers are carbonized and/or graphitized, whereby the handling of these fibers is made easy and at the same time high quality carbon fibers (including graphitized fibers; this shall apply hereinafter) can be produced.